Find the best answers to your questions with the help of IDNLearn.com's expert contributors. Get accurate and comprehensive answers to your questions from our community of knowledgeable professionals.
Sagot :
Sure, let's go through the details of solving this step-by-step.
### Step 1: Simplify the Fractions
First, let's simplify the fractions given in the expressions.
- The fraction [tex]\(-\frac{15}{5}\)[/tex] simplifies to [tex]\(-3\)[/tex] because [tex]\( \frac{15}{5} = 3 \)[/tex] and applying the minus sign gives [tex]\(-3\)[/tex].
- The fraction [tex]\(\frac{3}{5}\)[/tex] stays the same since it is already in its simplest form.
- The fraction [tex]\(-\frac{18}{5}\)[/tex] stays the same as well as it is also in its simplest form.
### Step 2: Perform the Divisions
We need to assess the result of the division of the dividends by the divisors:
#### Expression 1: [tex]\(-\frac{15}{5} - \frac{3}{5}\)[/tex]
1. Simplify [tex]\(-\frac{15}{5}\)[/tex] to get [tex]\(-3\)[/tex].
2. The fraction [tex]\(-\frac{3}{5}\)[/tex] remains as [tex]\(-\frac{3}{5}\)[/tex].
To divide [tex]\(-3\)[/tex] by [tex]\(\left(-\frac{3}{5}\right)\)[/tex]:
[tex]\[ -3 \div \left(-\frac{3}{5}\right) \][/tex]
To divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(-\frac{3}{5}\)[/tex] is [tex]\(-\frac{5}{3}\)[/tex]:
[tex]\[ -3 \times \left(-\frac{5}{3}\right) \][/tex]
Multiplying these terms, we get:
[tex]\[ -3 \times -\frac{5}{3} = \frac{15}{3} = 5.0 \][/tex]
So, the result of this division is [tex]\(5.0\)[/tex].
#### Expression 2: [tex]\(-\frac{15}{5} + \frac{3}{5}\)[/tex]
1. Simplify [tex]\(-\frac{15}{5}\)[/tex] to get [tex]\(-3\)[/tex].
2. The fraction [tex]\(\frac{3}{5}\)[/tex] remains as [tex]\(\frac{3}{5}\)[/tex].
Adding [tex]\(-3\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[ -3 + \frac{3}{5} \][/tex]
To add these, convert [tex]\(-3\)[/tex] to a fraction with a common denominator:
[tex]\[ -3 = \frac{-3 \times 5}{5} = \frac{-15}{5} \][/tex]
Now, add the fractions:
[tex]\[ \frac{-15}{5} + \frac{3}{5} = \frac{-15 + 3}{5} = \frac{-12}{5} = -2.4 \][/tex]
So, the result of this addition is [tex]\(-2.4\)[/tex].
### Step 3: Third Expression [tex]\(-\frac{18}{5}\)[/tex]
This fraction is already in simplified form, so the result remains:
[tex]\[ -\frac{18}{5} = -3.6 \][/tex]
### Step 4: Provided Additional Numbers
The numbers 9 and 12 are given and, based on the context, they appear to be results for specific parts of another question or steps provided:
[tex]\[ \text{Result 1: } 9 \][/tex]
[tex]\[ \text{Result 2: } 12 \][/tex]
### Final Results
After performing the operations and verifying the calculations, we have the following results:
- The division result of [tex]\(-\frac{15}{5}\)[/tex] by [tex]\(-\frac{3}{5}\)[/tex] is [tex]\(5.0\)[/tex].
- The addition result of [tex]\(-\frac{15}{5}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] is [tex]\(-2.4\)[/tex].
- The simplified fraction [tex]\(-\frac{18}{5}\)[/tex] remains [tex]\(-3.6\)[/tex].
- The given results 9 and 12.
Thus, the final set of results is:
[tex]\[ (5.0, -2.4, -3.6, 9, 12) \][/tex]
### Step 1: Simplify the Fractions
First, let's simplify the fractions given in the expressions.
- The fraction [tex]\(-\frac{15}{5}\)[/tex] simplifies to [tex]\(-3\)[/tex] because [tex]\( \frac{15}{5} = 3 \)[/tex] and applying the minus sign gives [tex]\(-3\)[/tex].
- The fraction [tex]\(\frac{3}{5}\)[/tex] stays the same since it is already in its simplest form.
- The fraction [tex]\(-\frac{18}{5}\)[/tex] stays the same as well as it is also in its simplest form.
### Step 2: Perform the Divisions
We need to assess the result of the division of the dividends by the divisors:
#### Expression 1: [tex]\(-\frac{15}{5} - \frac{3}{5}\)[/tex]
1. Simplify [tex]\(-\frac{15}{5}\)[/tex] to get [tex]\(-3\)[/tex].
2. The fraction [tex]\(-\frac{3}{5}\)[/tex] remains as [tex]\(-\frac{3}{5}\)[/tex].
To divide [tex]\(-3\)[/tex] by [tex]\(\left(-\frac{3}{5}\right)\)[/tex]:
[tex]\[ -3 \div \left(-\frac{3}{5}\right) \][/tex]
To divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(-\frac{3}{5}\)[/tex] is [tex]\(-\frac{5}{3}\)[/tex]:
[tex]\[ -3 \times \left(-\frac{5}{3}\right) \][/tex]
Multiplying these terms, we get:
[tex]\[ -3 \times -\frac{5}{3} = \frac{15}{3} = 5.0 \][/tex]
So, the result of this division is [tex]\(5.0\)[/tex].
#### Expression 2: [tex]\(-\frac{15}{5} + \frac{3}{5}\)[/tex]
1. Simplify [tex]\(-\frac{15}{5}\)[/tex] to get [tex]\(-3\)[/tex].
2. The fraction [tex]\(\frac{3}{5}\)[/tex] remains as [tex]\(\frac{3}{5}\)[/tex].
Adding [tex]\(-3\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[ -3 + \frac{3}{5} \][/tex]
To add these, convert [tex]\(-3\)[/tex] to a fraction with a common denominator:
[tex]\[ -3 = \frac{-3 \times 5}{5} = \frac{-15}{5} \][/tex]
Now, add the fractions:
[tex]\[ \frac{-15}{5} + \frac{3}{5} = \frac{-15 + 3}{5} = \frac{-12}{5} = -2.4 \][/tex]
So, the result of this addition is [tex]\(-2.4\)[/tex].
### Step 3: Third Expression [tex]\(-\frac{18}{5}\)[/tex]
This fraction is already in simplified form, so the result remains:
[tex]\[ -\frac{18}{5} = -3.6 \][/tex]
### Step 4: Provided Additional Numbers
The numbers 9 and 12 are given and, based on the context, they appear to be results for specific parts of another question or steps provided:
[tex]\[ \text{Result 1: } 9 \][/tex]
[tex]\[ \text{Result 2: } 12 \][/tex]
### Final Results
After performing the operations and verifying the calculations, we have the following results:
- The division result of [tex]\(-\frac{15}{5}\)[/tex] by [tex]\(-\frac{3}{5}\)[/tex] is [tex]\(5.0\)[/tex].
- The addition result of [tex]\(-\frac{15}{5}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] is [tex]\(-2.4\)[/tex].
- The simplified fraction [tex]\(-\frac{18}{5}\)[/tex] remains [tex]\(-3.6\)[/tex].
- The given results 9 and 12.
Thus, the final set of results is:
[tex]\[ (5.0, -2.4, -3.6, 9, 12) \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.
